Related papers: Unstable attractors in manifolds
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We study well-posedness and long-time dynamics of a class of quasilinear wave equations with a strong damping. We accept the Kirchhoff hypotheses and assume that the stiffness and damping coefficients are $C^1$ functions of the $L_2$-norm…
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global…
In this work, we study ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior, the main feature is a condition of transversality between unstable leaves when projected by the stable…
For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are…
Continuing a line of investigation initiated by Texier and Zumbrun on dynamics of viscous shock and detonation waves, we show that a linearly unstable Lax-type viscous shock solution of a semilinear strictly parabolic system of conservation…
Let $U\subset K$ be an open and dense subset of a compact metric space and let $\{\Phi_t\}_{t\ge0}$ be a Markov semigroup on the space of bounded Borel measurable functions on $U$ with the strong Feller property. Suppose that for each…
In this work, we analyze the asymptotic behavior of the attractors associated with a semilinear parabolic equation subject to homogeneous Neumann boundary conditions and defined on a thin domain $R^\varepsilon \subset \mathbb{R}^{1+n}$. We…
We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This…
We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the \emph{basic reproduction number} $\mathcal{R}_0 < 1$ is not sufficient to guarantee the elimination of…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless…
Given an embedded stable hypersurface in a four-dimensional symplectic manifold, we prove that it is stable isotopic to a $C^0$-close stable hypersurface with the following property: $C^\infty$-nearby hypersurfaces are generically unstable.…
Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We…
We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in…
This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…